Yeah there is an element of that, but I don't think it's entirely controversial to say that it all gets old very quickly.
Critical thinking takes work and research, which is fine for a specific topic or when you're reading something with existing context like something historic... but keeping on top of something where all the belligerents are pushing out narrative on a daily basis becomes fucking soul-destroying to fact-check and evaluate.
I don't think this is a "both sides" fallacy. It's just being super fed up of the constant shitslinging and media manipulation.